\psset{unit=1,algebraic}
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\psaxes[ticks=none,labels=none]{<->}(0,0)(-0.5,-0.5)(3.5,2.5)
\psplot[linecolor=blue]{0.5}{3.1}{(x-1.8)^2+0.5}
\psline[linecolor=red,linestyle=dashed](1.8,0)(1.8,0.5)(0,0.5)
\psline[linecolor=red,linestyle=dashed](1,0)(1,1.14)(0,1.14)
\footnotesize
\psxTick[ticksize=-3pt 0,labelsep=3pt](1.8){x_0}
\psxTick[ticksize=-3pt 0,labelsep=3pt](1){x}
\psyTick[ticksize=-3pt 0,labelsep=3pt](0.5){f(x_0)}
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\psyTick[ticksize=0,labelsep=8pt](0.8){\rotateleft{\leq}}
\rput(0.5,0){$($}
\psxTick[ticksize=-3pt 0,labelsep=3pt](0.5){x_0-\delta}
\rput(3.1,0){$)$}
\psxTick[ticksize=-3pt 0,labelsep=3pt](3.1){x_0+\delta}
\psdot[linecolor=green](1.8,0.5)
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